In 1974, Bridge enumerated the more straightforward facettings of the regular polyhedra, including those of the dodecahedron.

In 2006, Inchbald described the basic theory of facetting diagrams for polyhedra. For some vertex, the diagram shows all the possible edges and facets (new faces) which may be used to form facettings of the original hull. It is dual to the dual polyhedron's stellation diagram, which shows all the possible edges and vertices for some face plane of the original core.